CN103684027B - Single-phase photovoltaic grid-connected inverter based on ripple power transfer and modulation control method - Google Patents

Abstract

The invention discloses a kind of single-phase photovoltaic grid-connected inverter and modulation control method based on ripple power transfer, based on the thought of " energy transfer ", by increase a control freedom degree in inverter, the secondary power of DC bus capacitor is transferred to inductance element, the novel inverter topological structure of structure based on ripple power transfer circuit. In conjunction with grid-connected current controlling unit, provide modulator approach and the system control strategy of this New Topological. Analytical proof, this New single-phase single-stage inverter can not only effectively be controlled secondary power disturbance, suppress the secondary ripple component of DC voltage, improve photovoltaic system efficiency and grid-connected current quality, and be alternating current in guarantee energy storage inductor, avoid the impact of inductance DC bias current on system reliability and efficiency. Emulation and experiment show reasonability and the validity of this novel inverter and modulation control strategy.

Description

Single-phase photovoltaic grid-connected inverter based on ripple power transfer and modulation control method

Technical field

The present invention relates to a kind of single-phase photovoltaic grid-connected inverter and modulation control method based on ripple power transfer.

Background technology

Photovoltaic system DC voltage ripple can cause following problem: 1) ripple voltage can cause capacitance temperature to raise,It is the greatest factor that causes capacitor to damage; 2) DC voltage corrugated waveguide causes in outer voltage controlled quentity controlled variable and comprisesHarmonic components, these harmonic components not only can not maintain the stable of DC voltage, and cause the ginseng of current inner loopExamine signal and have low-frequency harmonics disturbance; 3) for photovoltaic system current control ring, even if reference current medium and low frequency is disturbedMoving being inhibited, in modulation aspect, DC voltage ripple also cannot be neglected the impact of current tracking control performanceSlightly.

One, ideally single-phase bridge photovoltaic DC-to-AC converter DC voltage ripple is analyzed

The topological structure of traditional single phase bridge-type photovoltaic DC-to-AC converter as shown in Figure 1, makes line voltage u_sFor

u_s(t)＝U_scos(ωt)(1)

U in formula_sFor voltage peak, ω is voltage angle frequency.

When grid-connected with unity power factor, grid-connected current i_sFor

i_s(t)＝I_scos(ωt)(2)

I in formula_sFor grid-connected current peak value.

Inverter shown in Fig. 2 exports the instantaneous power p of electrical network to_gFor

$p_g\left(t\right)=u_g\left(t\right)\×i_g\left(t\right)=\frac{U_s{I}_s}{2}(1+\cos 2\mathrm{\ωt})---\left(3\right)$

Can find out that by formula (3) instantaneous power that inverter is input to electrical network contains DC componentWith exchange pointAmountTwo parts: the amplitude of AC compounent is U_sI_s/ 2, the twice that frequency is mains frequency; DC componentNumerical value be U_sI_s/2。

The instantaneous power P of inverter Inductor L_LCan be expressed as

$P_{L1}=-\frac{1}{2}\mathrm{\ωL}{I}_m^2\sin \left(2\mathrm{\ωt}\right)---\left(4\right)$

Ignore the loss of power device of inverter and diode D, according to power conservation, obtain the defeated of photovoltaic arrayGo out power instantaneous value P_pvEqual inverter outlet side instantaneous power p_gInstantaneous power P with Inductor L_L'sWith,

$p_{\mathrm{PV}}\left(t\right)=p_g\left(t\right)+\frac{\mathrm{\ω}{L}_1{I}_s^2\sin \left(2\mathrm{\ωt}\right)}{2}---\left(5\right)$

Formula (3) is brought into formula (5) known, photovoltaic array power output contains secondary ripple powerAnd

${\tilde{P}}_{\mathrm{PV}}\left(t\right)=\frac{I_s{U}_s}{2}\cos \left(2\mathrm{\ωt}\right)-\frac{\mathrm{\ω}{L}_1{I}_s^2\sin \left(2\mathrm{\ωt}\right)}{2}---\left(6\right)$

Due to cos in formula (6), (t) (2 ω t) two components are orthogonal, and two parts cannot be cancelled out each other with sin for 2 ω.Therefore, the secondary ripple power of inverter direct-flow sideOnly can cushion by DC filter capacitor C CPower waveform as shown in Figure 2. By Tu Ke get, the charge-discharge energy equation of DC bus capacitor C is

$\frac{1}{2}C(u_{\mathrm{dc}}{\left(t\right)}^2-{\stackrel{\‾}{U}}_{\mathrm{dc}}^2)=\underset{0}{\overset{t}{\∫}}{\tilde{p}}_{\mathrm{PV}}\left(t\right)\mathrm{dt}---\left(7\right)$

U in formula_dc(t) andBe respectively instantaneous voltage and the average voltage at filter capacitor C two ends.

From formula (7), DC capacitor voltage must contain secondary ripple component, the size of direct current capacitanceRipple component is had to material impact. If capacitance is too little, the voltage pulsation meeting of DC side is very large,This can make electrochemical capacitor bear larger ripple voltage, causes electric capacity heating, can shorten like this longevity of electrochemical capacitorLife. Select the capacitor of larger capacitance, can effectively suppress the size of ripple, but capacitance causes compared with senior generalThe ceiling capacity output point tracking velocity of photovoltaic cell is slack-off, and volume and the cost of electric capacity all can increase simultaneously.

Two, under non-ideality, the DC voltage ripple of single-phase bridge photovoltaic DC-to-AC converter is analyzed

Under line voltage non-ideality, the DC voltage ripple power of single-phase bridge photovoltaic DC-to-AC converter will increase.Line voltage exists in harmonic pollution situation, establishes line voltage to be

$u_g=u_g^1+\underset{n=N_{\min }}{\overset{N_{\max }}{\mathrm{\Σ}}}{u}_g^n=U_g^1\cos \left({\mathrm{\ω}}_{1}t\right)+\underset{n=N_{\min }}{\overset{N_{\max }}{\mathrm{\Σ}}}{U}_g^n\cos \left(n{\mathrm{\ω}}_{1}t\right)---\left(8\right)$

In formula,For fundamental current component and nth harmonic component,Respectively first-harmonic and the n timeThe amplitude of harmonic wave.

If photovoltaic DC-to-AC converter is only exported fundamental current, and output current is

$i_g\left(t\right)=I_g^1\cos ({\mathrm{\ω}}_{1}t+{\mathrm{\θ}}_g^1)---\left(9\right)$

In formula,For amplitude and the starting phase angle of inverter bridge leg AC output current.

According to formula (8) and formula (9), the instantaneous power P of photovoltaic DC-to-AC converter AC_gFor

$\begin{array}{c}{p}_g\left(t\right)=u_g{i}_g\\ ={U^1}_g{I^1}_g\cos \left({\mathrm{\ω}}_{1}t\right)\cos ({\mathrm{\ω}}_{1}t+{{\mathrm{\θ}}^1}_g)+\underset{n=N\min }{\overset{N\max }{\mathrm{\Σ}}}{U^n}_g{I^1}_g\cos \left(n{\mathrm{\ω}}_{1}t\right)\cos ({\mathrm{\ω}}_{1}t+{{\mathrm{\θ}}^1}_g)\\ =\frac{1}{2}{U^1}_g{I^1}_g\cos {{\mathrm{\θ}}^1}_g+\frac{1}{2}{U^1}_g{I^1}_g\cos ({2\mathrm{\ω}}_{1}t+{{\mathrm{\θ}}^1}_g)\\ +\frac{1}{2}\underset{n=N\min }{\overset{N\max }{\mathrm{\Σ}}}{U^n}_g{I^1}_g\left\{\cos \right[(n+1){\mathrm{\ω}}_{1}t+{{\mathrm{\θ}}^1}_g]+\cos [(n-1){\mathrm{\ω}}_{1}t-{{\mathrm{\θ}}^1}_g\left]\right\}\end{array}---\left(10\right)$

The instantaneous voltage u of photovoltaic DC-to-AC converter Inductor_LWith instantaneous power p_LBe respectively

$u_L\left(t\right)=L\frac{d_{i_g}}{d_t}=-L{\mathrm{\ω}}_1{I}_g^1\sin ({\mathrm{\ω}}_{1}t+{\mathrm{\θ}}_g^1)---\left(11\right)$

P_L＝u_Li_g(t)(12)

Bring formula (11) and formula (9) into formula (12),

$p_L=-\frac{1}{2}{\mathrm{\ω}}_{1}L{\left(I_g^1\right)}^2\sin (2{\mathrm{\ω}}_{1}t+{2\mathrm{\θ}}_g^1)---\left(13\right)$

According to power conservation, the instantaneous power of photovoltaic DC-to-AC converter DC side is instantaneous generated output p_gWith inductance L winkTime power P_LAnd,

$\begin{array}{c}{p}_{\mathrm{dc}}=\frac{1}{2}{U^1}_g{I^1}_g\cos {{\mathrm{\θ}}^1}_g\\ +\frac{1}{2}{U^1}_g{I^1}_g\cos ({2\mathrm{\ω}}_{1}t+{{\mathrm{\θ}}^1}_g)-\frac{1}{2}{\mathrm{\ω}}_{1}L{\left(I_g^1\right)}^2\sin ({2\mathrm{\ω}}_{1}t+{2\mathrm{\θ}}_g^1)\\ +\frac{1}{2}\underset{n=N\min }{\overset{N\max }{\mathrm{\Σ}}}{U^n}_g{I^1}_g\left\{\cos \right[(n+1){\mathrm{\ω}}_{1}t+{{\mathrm{\θ}}^1}_g]+\cos [(n-1){\mathrm{\ω}}_{1}t-{{\mathrm{\θ}}^1}_g\left]\right\}\end{array}---\left(14\right)$

Abbreviation formula (14), can obtain

$\begin{array}{c}{p}_{\mathrm{dc}}=\frac{1}{2}{U}_g^1{I}_g^1\cos {\mathrm{\θ}}_g^1\\ +\frac{1}{2}[U_g^1{I}_g^1\cos {\mathrm{\θ}}_g^1-{\mathrm{\ω}}_{1}L{\left(I_g^1\right)}^2\sin \left({2\mathrm{\θ}}_g^1\right)]\cos \left({2\mathrm{\ω}}_{1}t\right)\\ -\frac{1}{2}[U_g^1{I}_g^1\sin {\mathrm{\θ}}_g^1+{\mathrm{\ω}}_{1}L{\left(I_g^1\right)}^2\cos \left({2\mathrm{\θ}}_g^1\right)]\sin \left({2\mathrm{\ω}}_{1}t\right)\\ +\frac{1}{2}({\cos \mathrm{\θ}}_g^1+\sin {\mathrm{\θ}}_g^1)I_g^1\underset{n=N\min }{\overset{N\max }{\mathrm{\Σ}}}{U}_g^n\cos \left[(n+1){\mathrm{\ω}}_{1}t\right]\\ +\frac{1}{2}({\cos \mathrm{\θ}}_g^1-{\sin \mathrm{\θ}}_g^1)I_g^1\underset{n=N\min }{\overset{N\max }{\mathrm{\Σ}}}{U}_g^n\cos \left[(n-1){\mathrm{\ω}}_{1}t\right]\end{array}---\left(15\right)$

According to above analysis, can draw to draw a conclusion: 1) voltage harmonic main 3,5,7,11 etc. in electrical networkN=2k ± 1 time odd component, causes photovoltaic DC-to-AC converter DC side instantaneous power to be mainly 2,4,6,8 etc. evenOrder harmonic components; 2) because the harmonic component of line voltage is conventionally much smaller than fundametal compoment, DC side instantaneous powerHarmonic component still taking second harmonic as main; 3) in single-phase electrical network, 3 voltage harmonics are larger, than idealLine voltage situation, the second harmonic component of DC side instantaneous power increases to some extent.

Three, the impact of secondary power disturbance on photovoltaic parallel in system

Photovoltaic system DC voltage ripple can cause following problem: 1) ripple voltage can cause capacitance temperature to raise,It is the greatest factor that causes capacitor to damage; 2) DC voltage corrugated waveguide causes in outer voltage controlled quentity controlled variable and comprisesHarmonic components, these harmonic components not only can not maintain the stable of DC voltage, and cause the ginseng of current inner loopExamine signal and have low-frequency harmonics disturbance; 3) for photovoltaic system current regulator, even reference current medium and low frequencyDisturbance is inhibited, and in modulation aspect, DC voltage ripple also cannot on the impact of current tracking control performanceIgnore.

Photovoltaic array has nonlinear output characteristic, and its P-V characteristic equation is

$P_{\mathrm{pv}}=U_{\mathrm{pv}}{I}_{\mathrm{sc}}[1-c_1(e^{\frac{U_{\mathrm{pv}}}{c_2{U}_{\mathrm{oc}}}}-1)]---\left(16\right)$

$c_1=(1-I_m/I_{\mathrm{sc}})e^{\frac{U_m}{c_2{U}_{\mathrm{oc}}}}---\left(17\right)$

c₂＝(U_m/U_oc-1)[In(1-I_m/I_sc)]^-1(18)

In formula, P_pvFor photovoltaic array power output, U_pvPhotovoltaic array output voltage, I_sc、U_oc、I_mAnd U_mPointOutput current and the output voltage of short circuit current that Wei photovoltaic array, open-circuit voltage, maximum power point.

If the ripple component v in photovoltaic array output voltage_r, ignore the pressure drop of diode D, when photovoltaic array is stablizedOperate in maximum power point U_mTime, under secondary power disturbance, photovoltaic array output voltage U_pvFor

U_pv＝U_m+v_r(19)

Wushu (19) is brought formula (16) into, photovoltaic array peak power output P that can be under secondary power disturbance_pvmFor

$P_{\mathrm{pvm}}=(U_m+v_r)I_{\mathrm{sc}}[1-c_1(e^{\frac{U_m+v_r}{c_2{U}_{\mathrm{oc}}}}-1)]---\left(20\right)$

Can be obtained fom the above equation, when photovoltaic array operates in maximum power point, voltage ripple will cause photovoltaic array outputPower is lower than maximum power point, and power waveform as shown in Figure 3.

As can be seen from Figure 3, the ripple of DC voltage, causes photovoltaic cell operating point to deviate from maximum power point,Output mean power declines. The AC compounent of photovoltaic combining inverter output instantaneous power is inevitable, this ripplePower not only affects the efficiency of photovoltaic cell, and has reduced the service life of photovoltaic cell.

Four, the impact of secondary power disturbance on inverter instruction current

Single-phase single-grade photovoltaic parallel in system needs DC voltage outer shroud, and this Voltage loop is according to photovoltaic array power outputVariation change grid-connected current reference amplitude, with balance sysmte power. Direct current pressure ring control block diagram is as Fig. 4 instituteShow. In figure, U_mFor the maximum power point voltage value of photovoltaic system MPPT link output, U_PVFor DC voltage samplingValue, I_refFor DC voltage PI controls output controlled quentity controlled variable, this controlled quentity controlled variable becomes electric current after synchronizeing with line voltageThe reference current signal i of controlling unit_ref。

In Fig. 4, the maximum power point voltage of MPPT algorithm output is DC quantity, and according to formula (7), photovoltaic arrayOutput voltage U_pvIn but contain a large amount of secondary ripple components, thereby make error signal e_uComprise secondary rippleComposition. e_uThrough PI controller, obtain grid-connected current with reference to peak I_ref, with electrical network unit signal cos (ω t) multiplies each other,Obtain grid-connected current reference value i_ref, therefore, i_refCan comprise a large amount of triple-frequency harmonics compositions. And humorous in reference currentWave component can make the total percent harmonic distortion of inverter output current become large.

If V_rFor ripple voltage component v_rPeak value, and V_r＝3V，k_pAnd k_iBe respectively PI controller in Fig. 4Ratio and integral coefficient, and k_p＝0.5，k_i=25, obtain i according to Fig. 4_refAmplitude-versus-frequency curve as Fig. 5 instituteShow.

Fig. 5 shows under the disturbance of secondary ripple voltage, photovoltaic system output current reference signal i_refIn contain a large amount ofTriple-frequency harmonics, this disturbance must have a strong impact on the waveform quality of grid-connected electric current.

In order to limit the triple-frequency harmonics composition of reference current signal, the most succinct processing method is, at DC voltageIn the sampling channel of UPV, seal in low pass filter (LowPassFilter, LPF), utilize LPF filtering secondary lineWave voltage signal.

But theory analysis is known, at LPF type and exponent number, definite in the situation that, the cut-off frequency of LPF is lower,Filter effect is better, but can cause that like this time delay strengthens, and makes the dynamic response process of Voltage loop slack-off; Cutoff frequencyRate is higher, and dynamic response process is faster, but LPF reduces the damping capacity of harmonic signal. That is to say,Making increases LPF at DC voltage sampling element, if can not be by DC voltage ripple control in less scope,DC voltage ripple is still difficult to be effectively suppressed on the impact of photovoltaic system output reference current.

The impact of controlling is followed the tracks of in five secondary power disturbances on inverter current

Definition is S for the switch function of photovoltaic DC-to-AC converter frequency analysis, ideally, and inverter direct-flow sideVoltage u_dcWith AC voltage u_oPass be

u_o＝u_dcS(21)

For two level PWM voltage source inverters, its PWM modulated process essence is two logic SPWM modulation techniques. Fig. 6Provided the switch function of desirable DC voltage, and DC voltage comprises the inverter output electricity in ripple situationPress modulation signal u in figure_m(t) expression formula is

In formula, the amplitude that U is modulating wave, T is the Fourier analysis cycle, ω is modulating wave first-harmonic angular frequency,φ is starting phase angle. Fig. 6 intermediate cam carrier wave represents with subscript c, to show and the difference of modulating wave, i.e. and φ_cRepresent triangular carrier phase shift, k_cω represents its angular frequency.

The Fourier space expression formula of the S of switch function shown in Fig. 6:

By dual Fourier transformation, the dual Fourier expression formula that has obtained switch function S shown in Fig. 6 is

In formula, J₀() is 0 rank Bessel function, J_n() is n rank Bessel functions, and

$\left\{\begin{array}{c}{J}_0\left(x\right)=\underset{m=1}{\overset{\∞}{\mathrm{\Σ}}}{(-1)}^m\frac{x^{2m}}{2^{2m}\·{(m!)}^2}\\ J_n\left(x\right)=\underset{m=1}{\overset{\∞}{\mathrm{\Σ}}}{(-1)}^m\frac{x^{n+2m}}{2^{n+2m}\·m!\·(n+m)!}\end{array}\right.---\left(25\right)$

Switch function S is formed by 3 additions in formula (24), by only relevant with modulating wave angular frequency the 1st fixedJustice is fundametal compoment; Will be only and carrier angular frequency_cRelevant the 2nd is defined as carrier wave harmonic component; Will with tuneAngular frequency ω processed and carrier angular frequency_cAll relevant the 3rd is defined as sideband harmonic wave.

If the DC voltage that comprises ripple voltage is expressed as

$u_{\mathrm{dc}}=\stackrel{\‾}{u_{\mathrm{dc}}}+R\cos \left({\mathrm{\ω}}_{r}t\right)---\left(26\right)$

In formulaRepresent DC voltage average value, r represents ripple harmonic amplitude, ω_rRepresent ripple harmonic frequency.

In photovoltaic DC-to-AC converter, because modulating wave angular frequency is far smaller than carrier angular frequency_c, therefore, formula(24) in, the 2nd, the 3rd is high fdrequency component, ignores high fdrequency component and by formula (24) and (26) substitution formula (21)In, obtain

According to more than, in single-phase photovoltaic DC-to-AC converter DC voltage, mainly comprise DC component and 2,4, the evens such as 6Harmonic wave, and with DC component and secondary ripple content maximum. From formula (27), DC side ripple voltage not onlyCause AC voltage to comprise 3 subharmonic, and can make the amplitude of AC fundamental component and phase place all occur partiallyMove.

More than analyze and show, the ripple power of single-phase photovoltaic DC-to-AC converter, causes 1) produce line on DC bus capacitorWave voltage, this voltage not only can cause capacitance temperature to raise, and will reduce the efficiency of photovoltaic array; 2) lightThe reference signal of volt inverter ac output current exists low frequency taking three times as main harmonic disturbance; 3) modulatedIn journey, the ripple of DC voltage is introduced into output current, not only comprises harmonic wave, and fundamental voltage amplitude and phase placeBe offset. Therefore, be necessary very much to design a kind of New single-phase photovoltaic that can suppress ripple power influences contraryBecome device, single-phase photovoltaic grid-connected inverter and the modulation control method based on ripple power transfer involved in the present invention,Can effectively address this problem.

Summary of the invention

Technical problem to be solved by this invention is to provide a kind of single-phase photovoltaic grid-connected based on ripple power transferInverter and modulation control method, be somebody's turn to do single-phase photovoltaic grid-connected inverter and modulation control based on ripple power transferMethod can effectively suppress direct current biasing and three ripple components of grid-connected current, reduces grid-connected current harmonic distortionRate, improves and network electric energy quality.

The technical solution of invention is as follows:

Based on a single-phase photovoltaic grid-connected inverter for ripple power transfer, comprise in parallel with photovoltaic array outlet sideThree brachium pontis, energy storage inductor L2; Each brachium pontis is formed by connecting by 2 power switch:

The first brachium pontis is made up of power switch T3 and T4;

The second brachium pontis is made up of power switch T1 and T2; [the second brachium pontis is public brachium pontis, needs and the 3rd bridgeArm is coordinated and is ensured that ripple power transfer, to energy storage inductor L2, also needs and first by power switch T5, T6Brachium pontis is coordinated by power switch T3 and T4, completes invert function; ]

The 3rd brachium pontis is made up of power switch T5 and T6; [the 3rd brachium pontis forms power together with energy storage inductor L2Carry circuit; ]

The mid point of the first brachium pontis is that the mid point of a point and the second brachium pontis is that b point is 2 of single-phase photovoltaic grid-connected inverterIndividual output;

The mid point that the two ends of described energy storage inductor L2 connect respectively b point and the 3rd brachium pontis is m point;

Described power switch is MOSFET.

The rated current I of energy storage inductor_LEqual inverter AC rated current I_s, i.e. I_L＝I_s; Energy storage inductorInductance value beλ is that ripple power transfer coefficient [need to be selected λ according to design, in exampleWay is: in the photovoltaic system of our design, MPPT maximum power point tracking controlling unit has based on extremum search to be calculatedThe MPPT method of method realizes, and therefore all ripples all can not be eliminated, and need to meet the requirement that MPPT controls,Therefore we design λ=0.8; ], the first-harmonic angular frequency that ω is electrical network; U_sFor line voltage peak;

[photovoltaic DC-to-AC converter DC side ripple power is

In formula, PL2,Be respectively inductance instantaneous power amplitude and inverter ripple power magnitude.

For ease of design, while making photovoltaic DC-to-AC converter rated operation point, the rated current I of energy storage inductor_LEqual contraryBecome device AC rated current I_s, i.e. I_L＝I_s. Like this, at energy storage inductor rated current I_LTurn with ripple powerMove in the definite situation of coefficient lambda, the value of energy storage inductor is】

Input quantity comprises the output voltage instantaneous value u of photovoltaic array_pv, output current instantaneous value i_pvAnd line voltageInstantaneous value u_s; Output controlled quentity controlled variable comprisesWith；

Inverter is by controlling output quantityTracking, realize the electricity generate function of photovoltaic DC-to-AC converter,ObtainProcess is:

First photovoltaic array output voltage and current signal are inputed to MPPT link, MPPT controls and passes through baseRealize in the MPPT of extremum search algorithm, MPPT controls the direct current corresponding to maximum power point of output photovoltaic arrayVoltage reference signal; SecondlyDo, after difference, to control and obtain through PI with the DC voltage Upv of actual samplesGrid-connected current amplitude reference quantity I_ref, then, with electric network voltage phase signal multiplication, obtain grid-connected current reference quantityi_ref ^*; Grid-connected current reference signal i_ref ^*With actual grid-connected current sampled signal i_refDo after difference, humorous through accurate ratioThe controller that shakes, divided by Upv, is the output controlled quentity controlled variable of inversion control link by the output quantity of accurate proportion control；

Wherein the transfer function of accurate ratio resonant controller is

$G_{\mathrm{MPR}}\left(s\right)=k_p+\frac{{2k}_1\mathrm{\ξ\ωs}}{s^2+2\mathrm{\ξ\ωs}+{\mathrm{\ω}}^2}---\left(4.2\right)$

In formula, k_pFor proportionality coefficient, k_iFor integral coefficient, ξ is damped coefficient;

According to shifting ripple power demand, determine energy storage inductor L₂Reference current be

In formulaλ is ripple transfer ratio, and span is [0,1]; [in exampleλ＝0.8】L₁For grid-connected inductance;

Energy storage inductor L₂Current Control realized by the control of ratio resonance, the transfer function of ratio resonant controller is

$G_{\mathrm{PR}}=k_{\mathrm{Lp}}+\frac{k_{\mathrm{Li}}s}{s^2+{\left(2\mathrm{\ω}\right)}^2};$

In formula, k_LpFor proportionality coefficient, k_LiFor integral coefficient, [proportionality coefficient and integral coefficient are according to inductance parameters and controlPerformance indications processed are determined, are prior art]

The output quantity of proportion control in above formula, divided by Upv, is to the output controlled quentity controlled variable of energy storage inductor controlling unit。

4. a modulator approach for single-phase photovoltaic grid-connected inverter, is characterized in that, adopts unipolarity frequency doubling technology,Triangular carrier is compared with a pair of opposite polarity modulating wave, produce two pairs of complementary driving signals, drive respectivelyTwo brachium pontis of moving single-phase full bridge inversion; This modulator approach is based on claimed in claim 3 single-phase photovoltaic grid-connected contraryBecome the control method of device;

The wherein modulation signal a of the first brachium pontis, the second brachium pontis and the 3rd brachium pontis, b, m is obtained by following steps:

According toWith, utilize following formula to calculate the duty cycle signals d of three brachium pontis_a，d_b，d_m，

$\left\{\begin{array}{c}{u}_{\mathrm{ab}}^{*}=(d_a-d_b)U_{\mathrm{pv}}\\ u_L^{*}=(d_m-d_b)U_{\mathrm{pv}}\\ d_a+d_b=1\\ 0\≤d_k\≤1,k=a,b,m\end{array}\right.$

And utilizing normalization algorithm, dutycycle db, the da of three brachium pontis of guarantee inverter and dm span are in [0,1];Then, according to

$\left\{\begin{array}{c}{d}_a=\frac{x}{T_s}=\frac{1+a}{2}\\ d_b=\frac{y}{T_s}=\frac{1+b}{2}\\ d_m=\frac{z}{T_s}=\frac{1+m}{2}\end{array}\right.$

Determine the value of modulation signal a, b and m;

Finally, by modulation signal a, b and m and triangular carrier comparison, can obtain the driving letter of power deviceNumber, complete modulated process.

Beneficial effect:

Single-phase photovoltaic grid-connected inverter and modulation control method based on ripple power transfer of the present invention, by detailThe DC voltage ripple of single-phase full bridge photovoltaic DC-to-AC converter is analysed in segmentation, and face in many ways to photovoltaic generating systemRing; And by the thought of " energy transfer ", by increase a control freedom degree in inverter, by direct currentThe secondary power of lateral capacitance is transferred to inductance element, and the novel inverter of structure based on ripple power transfer circuit opened upFlutter structure. In conjunction with grid-connected current controlling unit, provide modulator approach and the system control strategy of this New Topological.Analytical proof, this New single-phase single-stage inverter can not only effectively be controlled secondary power disturbance, and then suppresses direct currentThe secondary ripple component of voltage, improves photovoltaic system efficiency and grid-connected current quality, and guarantee energy storage inductorElectric current is of ac, has avoided the DC bias current in energy storage inductor. Emulation and result verification this novel reverseBecome reasonability and the validity of device and control strategy.

Brief description of the drawings

Fig. 1 is single-phase single-grade photovoltaic parallel in system topology diagram;

Fig. 2 be DC filter capacitor power waveform curve just;

Fig. 3 is photovoltaic array power output waveform under secondary power disturbance;

Fig. 4 is DC voltage outer shroud control block diagram;

Fig. 5 is grid-connected reference current amplitude-versus-frequency curve under secondary power disturbance;

Fig. 6 is PWM modulated process equivalent schematic.

Fig. 7 is that single-phase single-grade photovoltaic combining inverter improves topology diagram;

Fig. 8 is that single-phase single-grade photovoltaic combining inverter improves the simulation waveform figure of topological structure [3 curve dividesBe not line voltage, inverter output current and energy storage inductor current waveform-upper figure amplitude large be electrical network electricityPress];

Fig. 9 is the schematic diagram that is related to of magnetic conductivity and direct current biasing;

Figure 10 is the Novel photovoltaic inverter topology schematic diagram based on ripple power transfer;

Figure 11 is the modulation algorithm schematic diagram of Novel photovoltaic inverter;

Figure 12 is that photovoltaic DC-to-AC converter power switch drives signal and inverter bridge output voltage waveforms;

Figure 13 is control system structured flowchart;

Figure 14 is photovoltaic DC-to-AC converter power output comparison diagram before and after the work of ripple carry circuit;

Figure 15 is DC voltage and energy storage inductor voltage current waveform;

Figure 16 is grid-connected current and voltage on line side waveform;

Figure 17 is the frequency analysis contrast signal of photovoltaic inverter grid-connected electric current before and after the work of ripple carry circuitFigure;

Figure 18 is the DC voltage experimental waveform of photovoltaic DC-to-AC converter before and after the work of ripple carry circuit;

Figure 19 is grid-connected current and the voltage on line side experimental waveform that does not add secondary Ripple Suppression strategy;

Figure 20 is grid-connected current and the voltage on line side reality that adds ripple carry circuit and secondary Ripple Suppression strategyTest waveform.

Detailed description of the invention

Below with reference to the drawings and specific embodiments, the present invention is described in further details:

Embodiment 1:

Photovoltaic DC-to-AC converter based on decoupling zero circuit improves topological structure

Based on the above analysis to secondary power disturbance, use for reference the ripple power transfer circuit of single phase rectifier circuit,Study and shown in Fig. 7, improved topological structure. This improvement photovoltaic DC-to-AC converter topological structure, on conventional full bridge basis,Increased secondary power decoupling zero circuit, and decoupling zero circuit is by 1 power switch T5,1 diode D2 and energy storage electricitySense L2 composition.

Inductive energy storage inductance L as seen from Figure 7₂Electric current for being only positive direction, energy storage inductor L₂Current i_LCanBe assumed to be

i_L＝I_L|cos(ωt-α)|(28)

I in formula_LFor current peak, α is angle of lag.

Inductance L₂Energy E_L2And power P_L2Can be expressed as

$E_{L2}=\frac{L_2{i}_L^2\left(t\right)}{2}---\left(29\right)$

$P_{L2}=-\frac{1}{2}\mathrm{\ω}{L}_2{I}_L^2\sin (2\mathrm{\ωt}-2\mathrm{\α})---\left(30\right)$

In like manner, grid-connected inductance L₁Power P_L1Can be expressed as

$P_{L1}=-\frac{1}{2}\mathrm{\ω}{L}_1{I}_s^2\sin \left(2\mathrm{\ωt}\right)---\left(31\right)$

If inverter unity power factor output current, ignores main circuit power attenuation, inverter both sides powerConservation, DC side power is divided into 3 parts, and available following relational expression is expressed:

$\begin{array}{c}{P}_{\mathrm{pv}}\left(t\right)=\frac{I_s{V}_s}{2}+\frac{I_s{V}_s}{2}\cos \left(2\mathrm{\ωt}\right)\\ -\frac{\mathrm{\ω}{L}_1{I}_s^2\sin \left(2\mathrm{\ωt}\right)}{2}\\ -\frac{\mathrm{\ω}{L}_2{I}_L^2\sin (2\mathrm{\ωt}-2\mathrm{\α})}{2}\end{array}---\left(32\right)$

If in formula (32) all AC compounents and be 0, the secondary ripple component of DC side power will obtain press downSystem, realizes the decoupling zero of alternating current-direct current power component, therefore order

$I_s{U}_s\cos \left(2\mathrm{\ωt}\right)-\mathrm{\ω}{L}_1{I}_s^2\sin \left(2\mathrm{\ωt}\right)=\mathrm{\ω}{L}_2{I}_L^2\sin (2\mathrm{\ωt}-2\mathrm{\α})---\left(33\right)$

Can be obtained fom the above equation, if inductance L₂Electric current I_LWith angle of lag α, meet relational expression:

$I_L=\sqrt{\sqrt{{\left(I_s{U}_s\right)}^2+{\left(\mathrm{\ω}{L}_1{I}_s^2\right)}^2}/\mathrm{\ω}{L}_2}---\left(34\right)$

In formula

Wushu (34) and (35) are brought formula (28) into, and inverter AC secondary ripple will be by inductance L₂Provide, andEnergy storage inductor L₂Current i_LFor:

According to above analysis, this topology and control method thereof only not only can ensure in photovoltaic array power outputContain DC component, and will largely reduce secondary ripple component in DC voltage, improve DC side electricityThe reliability of holding. Fig. 8 has provided the simulation experiment result of this topology photovoltaic DC-to-AC converter, and 3 curves are respectively electricityNet voltage, inverter output current and energy storage inductor current waveform.

According to theory analysis and simulation result, in energy storage inductor, electric current includes a large amount of DC components, Er QiesuiThe increase of single-phase photovoltaic DC-to-AC converter power output, the direct current biasing in energy storage inductor also increases thereupon.

But under DC bias current effect, due to saturation, the magnetic conductivity of energy storage inductor magnetic core isNow reduce trend. Fig. 9 has provided the affect trend of DC bias current on magnetic core magnetic conductivity. Direct current biasing electricityStream not only makes the magnetic conductivity of inductance element reduce, and can cause inductance core loss obviously to increase. Existing grindingStudy carefully result and show under identical AC magnetic field, the existence of DC bias magnetic field can produce and be several times as much as pure alternation magneticThe extra core loss of field. Therefore, DC bias current can not be ignored the impact of inductance.

Photovoltaic DC-to-AC converter New Topological and modulation strategy thereof based on ripple power transfer

In the photovoltaic DC-to-AC converter topology proposing, in energy storage inductor, there is larger DC bias current above. ForAvoid the direct current biasing bias current in energy storage inductor, this section proposes a kind of novel photovoltaic based on ripple power transferInverter topology, being intended to make the electric current in energy storage inductor is pure alternating current, New Topological is as Figure 10 instituteShow.

Visible compared with the circuit of decoupling zero shown in Fig. 7, many power switch in ripple power transfer circuit, shouldThe existence of switch, can flow with the direction of bearing inductive current. Therefore, establish energy storage inductor L₂Current i_LFor

i_L＝I_Lcos(ωt-α)(37)

I in formula_LFor current peak, α is angle of lag.

According to formula (37), photovoltaic DC-to-AC converter AC ripple power is

${\tilde{p}}_{\mathrm{ac}}\left(t\right)=\frac{I_s{V}_s}{2}\cos \left(2\mathrm{\ωt}\right)-\frac{\mathrm{\ω}{L}_1{I}_s^2\sin \left(2\mathrm{\ωt}\right)}{2}---\left(38\right)$

Photovoltaic DC-to-AC converter DC side ripple power is

${\tilde{p}}_{\mathrm{dc}}\left(t\right)={\tilde{p}}_C\left(t\right)-\frac{{\mathrm{\ωL}}_2{I}_L^2\sin (2\mathrm{\ωt}-2\mathrm{\α})}{2}---\left(39\right)$

In formula,For the ripple power of DC bus capacitor device.

According to power-balance, inverter exchanges all has DC side ripple to provide, and has

${\tilde{p}}_{\mathrm{dc}}\left(t\right)={\tilde{p}}_{\mathrm{ac}}\left(t\right)---\left(40\right)$

If ripple power transfer circuit is not worked, all ripple power of AC all has DC bus capacitor device to holdLoad,

${\tilde{p}}_{\mathrm{ac}}\left(t\right)={\tilde{p}}_C\left(t\right)---\left(41\right)$

The function of ripple power transfer circuit, is the ripple power transfer on capacitor to energy storage inductor,If ripple power transfer coefficient is λ, energy storage inductor power is

$p_{L2}=\mathrm{\λ}{\tilde{p}}_{\mathrm{dc}}\left(t\right)---\left(42\right)$

By formula (424) and formula (39) substitution formula (40), the ripple power that DC bus capacitor device bears is

${\tilde{p}}_C={\tilde{p}}_{\mathrm{dc}}\left(t\right)(1-\mathrm{\λ})---\left(43\right)$

According to shifting ripple power coefficient, if inductance L₂Electric current be

In formula

This Novel photovoltaic inverter topology, has not only effectively avoided direct current biasing to inductance element loss and propertyCan impact, and the electric current of energy storage inductor is pure AC compounent, the more important thing is the secondary of DC side powerRipple component is controllable, has left more selection space to designer.

In Figure 10,3 brachium pontis need to be exported two sinusoidal voltage waveforms. In modulation aspect, according to twoThe output voltage reference signal of knowing, calculates the dutycycle of 3 brachium pontis, needs constraints of Mathematics structural,Obtain the dutycycle of each switch.

If S_a、S_bAnd S_mRespectively the switch function of three brachium pontis: S_k=1, brachium pontis switch conduction in expression, underBrachium pontis switch turn-offs, wherein k=a, b, m; S_k=0, represent lower brachium pontis switch conduction, upper brachium pontis switch turn-offs.

Table 1 New Topological main circuit switch pattern

Taking o point as reference potential,

$\left\{\begin{array}{c}{u}_{\mathrm{ao}}=S_a{U}_{\mathrm{pv}}\\ u_{\mathrm{bo}}=S_b{U}_{\mathrm{pv}}\\ u_{\mathrm{mo}}=S_m{U}_{\mathrm{pv}}\end{array}\right.---\left(45\right)$

Can obtain u by table 1_abAnd u_LRelational expression be

$\left\{\begin{array}{c}{u}_{\mathrm{ab}}=(S_a-S_b)U_{\mathrm{pv}}\\ u_L=(S_m-S_b)U_{\mathrm{pv}}\end{array}\right.---\left(46\right)$

Get S_a、S_bAnd S_mDutycycle be respectively db, da and dm, utilize state averaging method-based modeling method, go upFormula can be converted into

$\left\{\begin{array}{c}{U}_{\mathrm{ab}}^{*}=(d_a-d_b)U_{\mathrm{pv}}\\ u_L^{*}=(d_m-d_b)U_{\mathrm{pv}}\\ 0\≤d_k\≤1,k=a,b,m\end{array}\right.---\left(47\right)$

In formula (47), comprise 3 variablees in two equations, therefore, different duty building method, canTo form different modulation strategies.

Unipolarity multiple-frequency modulation technology, compares triangular carrier with a pair of opposite polarity modulating wave, produce twoTo complementary driving signal, drive respectively two brachium pontis of single-phase full bridge inversion, make actual ripple frequency for openingClose 2 times of frequency. In order to reduce the frequency of switching tube, reduce switching loss, adopt unipolarity multiple-frequency modulation sideMethod, can improve the performance of Novel photovoltaic inverter. In bipolarity modulation, unipolarity multiple-frequency modulation algorithm,In inverter there is an inherent constraint in the dutycycle db of inverter bridge leg and da,

d_a+d_b＝1(48)

In modulation algorithm implementation procedure, first according to the u of control strategy output_ab、u_LReference value, utilize formula (47) and(48) and normalization algorithm, calculate dutycycle db, da and the dm of three brachium pontis of inverter.

Figure 11 has provided at u_ab0，u_LNovel photovoltaic DC-to-AC converter unipolarity multiple-frequency modulation general principle when < 0.In figure, a, b and m are respectively the modulation signal of right side brachium pontis, middle brachium pontis and left side brachium pontis, y, x and zBe respectively each switch periods VT₁、VT₃And VT₅ON time. Can draw following equation according to Figure 11Formula

$\left\{\begin{array}{c}{d}_a=\frac{x}{T_s}=\frac{1+a}{2}\\ d_b=\frac{y}{T_s}=\frac{1+b}{2}\\ d_m=\frac{z}{T_s}=\frac{1+m}{2}\end{array}\right.---\left(49\right)$

According to formula (49), can determine the value of comparison signal a, b and m.

Novel photovoltaic grid-connected inverter simulation result and experimental result

In order to verify photovoltaic DC-to-AC converter New Topological based on ripple power transfer and the validity of modulation strategy thereof,Based on Matlab/Simulink simulation software, build system simulation model, system relevant parameter is as table 2Shown in.

Table 2 photovoltaic generation analogue system relevant parameter

Figure 12 provides the switching signal of VT1 in photovoltaic DC-to-AC converter, VT2, VT3, and inverter bridge output voltage U_abAnd U_LOutput voltage instantaneous value, waveform show Novel photovoltaic grid-connected inverter realized frequency multiplication output.

Photovoltaic parallel inverter control system structure as shown in figure 13, adopt by MPPT maximum power point tracking (MPPT) moduleUse extremum search algorithm,Obtained by MPPT and grid-connected current control module; In figure, dotted line frame inside is divided into lineWave power carry circuit controlling unit, by u_sAnd i_sThrough formula (44) energy storage inductor current reference signal. Due to electric currentError signal e_LFor of ac, and contain low order even-order harmonic, this link controller adoption rate resonant controller(PR), its biography letter is

$G_{\mathrm{PR}}=k_p+\frac{k_{h}s}{s^2+{\left(2\mathrm{\&omega;}\right)}^2}---\left(45\right)$

The intensity of illumination that photovoltaic array is set is 800W/m², temperature is 25 DEG C, decoupling zero circuit is in the time of t=0.3sStart working. Figure 14 has provided before and after the work of ripple carry circuit, the contrast waveform of photovoltaic array power output.

Power waveform in Figure 14 shows: before the work of ripple carry circuit, photovoltaic array power output existsSecondary power disturbance, power average value is 764.5W; Before the work of ripple carry circuit, secondary power disturbance obtainsTo suppressing, power output is 773.5WW, and ripple carry circuit has improved the power stage of photovoltaic DC-to-AC converter.

Figure 15 has provided the photovoltaic DC-to-AC converter energy storage inductor L based on ripple power transfer circuit₂With DC voltageVoltage current waveform. As seen from the figure, system transient modelling process time is less than 0.1s, before the work of ripple carry circuit,DC voltage secondary ripple component peak-to-peak value is up to 24V; After the work of ripple carry circuit, secondary ripple voltage peakPeak value is reduced to 4V, and in DC voltage, secondary ripple component obtains larger inhibition, and the large I of this ripple is by lineRipple rejection coefficient is controlled. Energy storage inductor L₂Electric current do not comprise DC component, effectively suppressed direct current inclined to one sidePut the impact of electric current on inductance magnetic conductivity and efficiency, according to voltage u_LPositive and negative selection charging and discharging, discharge and rechargeCurrent i_LMeet formula (44).

Figure 16 has provided alternating current voltage on line side u_sWith grid-connected current i_sWaveform, i_sAnd u_sWith frequency homophase, realizeUnity power factor control. Figure 17 has given the frequency analysis of photovoltaic inverter grid-connected electric current. By Figure 15,16Visible, while not adding secondary power suppression strategy, ripple carry circuit is not worked, i_sIn contain a large amount of straightStream biasing and triple-frequency harmonics, percent harmonic distortion (THD) is 2.91%; Add after secondary power suppression strategy,After the work of ripple carry circuit, DC component and the triple-frequency harmonics of grid-connected current are inhibited, and THD is reduced to2.48％。

According to above simulation result with analyze knownly, add the single-phase single-grade photovoltaic parallel in system of ripple carry circuitOutput characteristics be very significantly improved, the disturbance of DC side secondary power and secondary DC ripple voltage obtain largerSuppress, direct current biasing and the harmonic component of AC output current are all inhibited. The design of ripple carry circuit,Photovoltaic generating system energy utilization efficiency and grid-connected current quality are improved.

DC voltage experimental waveform as shown in figure 18, adds after secondary Ripple Suppression strategy ripple carry circuitWork, ripple voltage peak-to-peak value is 1.2V; After ripple carry circuit quits work, ripple voltage peak-to-peak value is highReach 5.8V. As can be seen here, ripple carry circuit can suppress the ripple component of DC voltage effectively.

Figure 19 has provided the grid-connected current and the voltage on line side waveform that do not add secondary Ripple Suppression strategy, grid-connected electricityAlthough stream with frequency homophase, has been realized unity power factor control with voltage on line side, contains a large amount of triple-frequency harmonics.

Figure 20 has provided the grid-connected current and the voltage on line side that add ripple carry circuit and secondary Ripple Suppression strategyWaveform, grid-connected current and voltage on line side, with frequency homophase, have been realized unity power factor control. Due to DC voltageSecondary ripple component is inhibited, and the triple-frequency harmonics content in grid-connected current is very little.

In the situation that external condition is identical, add the peak-to-peak value of the grid-connected current of secondary Ripple Suppression strategy to compare notAdd the large 0.7A of peak-to-peak value of the grid-connected current of secondary Ripple Suppression strategy, the power output of photovoltaic system improves4%. Experimental result shows, ripple carry circuit can suppress the secondary ripple component of DC voltage well,Improve the quality of grid-connected current and the efficiency of photovoltaic system.

Conclusion

The present invention, by the analysis to conventional single-phase single-grade photovoltaic parallel in system secondary power disturbance, has studied baseIn the improvement topological structure of the single-phase single-grade photovoltaic combining inverter of secondary power decoupling zero circuit, on this topology basisUpper, for solving the DC offset problem of energy storage inductor in decoupling zero circuit, propose based on ripple power transfer circuitNovel photovoltaic inverter topology, this New Topological by the transfer control to secondary power, is ensureing storageCan in inductance, not contain under the prerequisite of DC bias current, effectively reduced photovoltaic array power output and direct currentThe secondary ripple component of voltage, thus direct current biasing and three ripple components of grid-connected current suppressed, reduceGrid-connected current percent harmonic distortion, has improved and network electric energy quality. Emulation and experiment show this ripple powerThe validity of carry circuit and modulation strategy and superiority.

Claims (2)

1. the single-phase photovoltaic grid-connected inverter based on ripple power transfer, is characterized in that, comprises with photovoltaic array and exportingThree brachium pontis of side parallel connection, energy storage inductor L2; Each brachium pontis is formed by connecting by 2 power switch:

The first brachium pontis is made up of power switch T3 and T4;

The second brachium pontis is made up of power switch T1 and T2;

The 3rd brachium pontis is made up of power switch T5 and T6;

The mid point of the first brachium pontis is that the mid point of a point and the second brachium pontis is 2 outputs that b point is single-phase photovoltaic grid-connected inverterEnd;

The mid point that the two ends of described energy storage inductor L2 connect respectively b point and the 3rd brachium pontis is m point;

Described power switch is MOSFET;

The rated current I of energy storage inductor_LEqual inverter AC rated current I_s, i.e. I_L＝I_s; The inductance of energy storage inductorValue isλ is ripple power transfer coefficient, the first-harmonic angular frequency that ω is electrical network; U_sFor line voltage peak;

Input quantity comprises the output voltage instantaneous value u of photovoltaic array_pv, output current instantaneous value i_pvWith line voltage instantaneous valueu_s; Output controlled quentity controlled variable comprisesWith

Inverter is by output controlled quentity controlled variableTracking, realize the electricity generate function of photovoltaic DC-to-AC converter,Acquisition process be:

First photovoltaic array output voltage and current signal are inputed to MPPT link, MPPT controls by searching based on extreme valueThe MPPT algorithm of rope is realized, and MPPT controls the DC voltage reference signal corresponding to maximum power point of output photovoltaic arraySecondlyDo, after difference, to control and obtain grid-connected current amplitude reference quantity through PI with the DC voltage Upv of actual samplesI_ref, then, with electric network voltage phase signal multiplication, obtain grid-connected current reference quantityGrid-connected current reference signalWith actual grid-connected current sampled signal i_refDo after difference, through accurate ratio resonant controller, by the output quantity of accurate proportion controlDivided by Upv, be the output controlled quentity controlled variable of inversion control link

Wherein the transfer function of accurate ratio resonant controller is

$G_{MPR}\left(s\right)=k_p+\frac{2k_I\mathrm{\&xi;}\mathrm{\&omega;}s}{s^2+2\mathrm{\&xi;}\mathrm{\&omega;}s+{\mathrm{\&omega;}}^2}---\left(4.2\right)$

In formula, k_pFor proportionality coefficient, k_IFor integral coefficient, ξ is damped coefficient;

According to shifting ripple power demand, determine energy storage inductor L₂Reference current be

In formulaSpan is [0,1]; L₁For grid-connected inductance;

Energy storage inductor L₂Current Control realized by the control of ratio resonance, the transfer function of ratio resonant controller isIn formula, k_LpFor proportionality coefficient, k_LiFor integral coefficient;

The output quantity of proportion control in above formula, divided by Upv, is to the output controlled quentity controlled variable of energy storage inductor controlling unit

2. a modulator approach for single-phase photovoltaic grid-connected inverter, is characterized in that, adopts unipolarity frequency doubling technology, by triangleCarrier wave is compared with a pair of opposite polarity modulating wave, produces two pairs of complementary driving signals, drives respectively single-phase full bridge contraryTwo brachium pontis that become; The control method of this modulator approach based on single-phase photovoltaic grid-connected inverter claimed in claim 1;

The wherein modulation signal a of the first brachium pontis, the second brachium pontis and the 3rd brachium pontis, b, m is obtained by following steps:

According toWithUtilize following formula to calculate the duty cycle signals d of three brachium pontis_a,d_b,d_m,

$\left\{\begin{array}{c}{u}_{ab}^{*}=(d_a-d_b)U_{pv}\\ u_L^{*}=(d_m-d_b)U_{pv}\\ d_a+d_b=1\\ 0\&le;d_k\&le;1,k=a,b,m\end{array}\right.$

And utilizing normalization algorithm, dutycycle db, the da of three brachium pontis of guarantee inverter and dm span are in [0,1];

Then, according to $\left\{\begin{array}{c}{d}_a=\frac{1+a}{2}\\ d_b=\frac{1+b}{2}\\ d_m=\frac{1+m}{2}\end{array}\right.$ Determine the value of modulation signal a, b and m;

Finally, by modulation signal a, b and m and triangular carrier comparison, can obtain the driving signal of power device, completeBecome modulated process.